IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes

Listed author(s):
  • Qin Zhou
  • Changliang Zou
  • Zhaojun Wang
  • Wei Jiang
Registered author(s):

    Many applications involve monitoring incidence rates of the Poisson distribution when the sample size varies over time. Recently, a couple of cumulative sum and exponentially weighted moving average (EWMA) control charts have been proposed to tackle this problem by taking the varying sample size into consideration. However, we argue that some of these charts, which perform quite well in terms of average run length (ARL), may not be appealing in practice because they have rather unsatisfactory run length distributions. With some charts, the specified in-control (IC) ARL is attained with elevated probabilities of very short and very long runs, as compared with a geometric distribution. This is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs, which, in turn, hurt an operator's confidence in valid alarms. Furthermore, with many charts, the IC ARL exhibits considerable variations with different patterns of sample sizes. Under the framework of weighted likelihood ratio test, this article suggests a new EWMA control chart which automatically integrates the varying sample sizes with the EWMA scheme. It is fast to compute, easy to construct, and quite efficient in detecting changes of Poisson rates. Two important features of the proposed method are that the IC run length distribution is similar to that of a geometric distribution and the IC ARL is robust to various patterns of sample size variation. Our simulation results show that the proposed chart is generally more effective and robust compared with existing EWMA charts. A health surveillance example based on mortality data from New Mexico is used to illustrate the implementation of the proposed method. This article has online supplementary materials.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

    Volume (Year): 107 (2012)
    Issue (Month): 499 (September)
    Pages: 1049-1062

    in new window

    Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1049-1062
    DOI: 10.1080/01621459.2012.682811
    Contact details of provider: Web page:

    Order Information: Web:

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1049-1062. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.